Find general solutions (implicit if necessary, explicit if conve- nient) of the differential equations in Problems...

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Find general solutions (implicit if necessary, explicit if conve- nient) of the differential equations in Problems 1 through 18. Primes denote derivatives with respect to x. dy 1. +2xy =01 dx dy dx 3. 5. = y sin x dy 7. = dx = (64xy)1/3 = √1-y² dx (2) 11. y'=xy³ 13. dy 15. = dx dy dx = 2y = (y+ + 1) cos x (x-1)ys x² (2y3 -y) dy dx 4. (1+x) dy dx dy dx 2. 6. 8. + 2xy² = 0 dy dx = 4y = 3√ √xy = 2x sec y = 10. (1+x)² = (1+y)² dx 12. yy' = x(y² +1) dy 1+ √√x 14. dx 1 + √F 16. (x²+ 1)(tan y)y' = = X 17. y' = 1+x+y+xy (Suggestion: Factor the right-hand side.) 18. x² y'=1-x² + y²-x²2 Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy 19. = yet, y(0) = 2e dx dy 20. = 3x²(y² + 1), dx 21. 2y 22. 23. X dx √x²-16 24. dy dx dx dy dx y(0) = 1 y (5) = 2 = 4x³y- y. y(1) = -3 +1= 2y. y(1) = 1 =ycoLx, y(z)=ấn Find general solutions (implicit if necessary, explicit if conve- nient) of the differential equations in Problems 1 through 18. Primes denote derivatives with respect to x. dy 1. +2xy =01 dx dy dx 3. 5. = y sin x dy 7. = dx = (64xy)1/3 = √1-y² dx (2) 11. y'=xy³ 13. dy 15. = dx dy dx = 2y = (y+ + 1) cos x (x-1)ys x² (2y3 -y) dy dx 4. (1+x) dy dx dy dx 2. 6. 8. + 2xy² = 0 dy dx = 4y = 3√ √xy = 2x sec y = 10. (1+x)² = (1+y)² dx 12. yy' = x(y² +1) dy 1+ √√x 14. dx 1 + √F 16. (x²+ 1)(tan y)y' = = X 17. y' = 1+x+y+xy (Suggestion: Factor the right-hand side.) 18. x² y'=1-x² + y²-x²2 Find explicit particular solutions of the initial value problems in Problems 19 through 28. dy 19. = yet, y(0) = 2e dx dy 20. = 3x²(y² + 1), dx 21. 2y 22. 23. X dx √x²-16 24. dy dx dx dy dx y(0) = 1 y (5) = 2 = 4x³y- y. y(1) = -3 +1= 2y. y(1) = 1 =ycoLx, y(z)=ấn

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